{"id":33109,"date":"2025-06-23T06:37:38","date_gmt":"2025-06-23T06:37:38","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=33109"},"modified":"2025-06-23T06:37:40","modified_gmt":"2025-06-23T06:37:40","slug":"select-all-expressions-that-are-equivalent-to-6x-1-3x-1","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/select-all-expressions-that-are-equivalent-to-6x-1-3x-1\/","title":{"rendered":"Select all expressions that are equivalent to 6x +1 – (3x – 1)"},"content":{"rendered":"\n

Select all expressions that are equivalent to 6x +1 – (3x – 1) Hint: Don’t forget to distribute the negative! 6x +1 -3.2 – 1 6x + (-3x) +1+1 3x + 2 6x – 3x + 1 – 1 6x +1+(-3x) \u2013 (-1)<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s solve this step by step and check which expressions are equivalent to 6x + 1 – (3x – 1)<\/strong>.<\/p>\n\n\n\n

Step 1: Simplify the Original Expression<\/h3>\n\n\n\n

The expression is:
6x + 1 – (3x – 1)<\/strong><\/p>\n\n\n\n

Distribute the negative sign:
6x + 1 – 3x + 1<\/strong><\/p>\n\n\n\n

Combine like terms:
6x – 3x + 1 + 1 = 3x + 2<\/strong><\/p>\n\n\n\n

So, the simplified form is:
3x + 2<\/strong><\/p>\n\n\n\n

Step 2: Check Each Option<\/h3>\n\n\n\n

Option 1:<\/strong>
6x + 1 – 3.2 – 1<\/strong>
Notice the term 3.2<\/strong>, which is a decimal. Our expression uses 3x<\/strong>, not 3.2<\/strong>, so this is not equivalent<\/strong>.<\/p>\n\n\n\n

Option 2:<\/strong>
6x + (-3x) + 1 + 1<\/strong>
Simplify:
6x – 3x + 1 + 1 = 3x + 2<\/strong>
This matches the simplified form, so this is equivalent<\/strong>.<\/p>\n\n\n\n

Option 3:<\/strong>
3x + 2<\/strong>
This is the same as our simplified form, so this is equivalent<\/strong>.<\/p>\n\n\n\n

Option 4:<\/strong>
6x – 3x + 1 – 1<\/strong>
Simplify:
6x – 3x + 1 – 1 = 3x + 0 = 3x<\/strong>
This does not<\/strong> match 3x + 2<\/strong>, so it is not equivalent<\/strong>.<\/p>\n\n\n\n

Option 5:<\/strong>
6x + 1 + (-3x) – (-1)<\/strong>
Simplify step by step:
6x + 1 – 3x + 1 = 3x + 2<\/strong>
This matches the simplified form, so this is equivalent<\/strong>.<\/p>\n\n\n\n

Final Answer<\/h3>\n\n\n\n

The expressions that are equivalent to 6x + 1 – (3x – 1)<\/strong> are:
\u2714 6x + (-3x) + 1 + 1<\/strong>
\u2714 3x + 2<\/strong>
\u2714 6x + 1 + (-3x) – (-1)<\/strong><\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

When simplifying algebraic expressions, it is essential to handle negative signs properly, especially when parentheses are involved. In the given expression 6x + 1 – (3x – 1)<\/strong>, the parentheses mean that everything inside must be affected by the negative sign placed in front. Distributing the negative sign changes 3x – 1<\/strong> to -3x + 1<\/strong>.<\/p>\n\n\n\n

This results in 6x + 1 – 3x + 1<\/strong>, which simplifies by combining like terms. The terms involving x<\/strong> are 6x<\/strong> and -3x<\/strong>, which add to 3x<\/strong>. The constant terms 1<\/strong> and 1<\/strong> add to 2<\/strong>, giving the simplified expression 3x + 2<\/strong>.<\/p>\n\n\n\n

To determine which given expressions are equivalent, each option must be simplified and compared to 3x + 2<\/strong>. Expressions that involve decimals like 3.2<\/strong> are immediately ruled out because they differ in form and value.<\/p>\n\n\n\n

Correct expressions use proper distribution and grouping of terms. For example, 6x + (-3x) + 1 + 1<\/strong> simplifies directly to 3x + 2<\/strong>, matching the original simplified form. Similarly, 6x + 1 + (-3x) – (-1)<\/strong> becomes 3x + 2<\/strong> after simplifying both the variables and constants.<\/p>\n\n\n\n

Incorrect expressions fail to simplify to 3x + 2<\/strong>. For instance, 6x – 3x + 1 – 1<\/strong> simplifies to 3x<\/strong>, missing the constant term +2<\/strong>, making it non-equivalent.<\/p>\n\n\n\n

Thus, understanding distribution and combining like terms is crucial to finding equivalent expressions accurately.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Select all expressions that are equivalent to 6x +1 – (3x – 1) Hint: Don’t forget to distribute the negative! 6x +1 -3.2 – 1 6x + (-3x) +1+1 3x + 2 6x – 3x + 1 – 1 6x +1+(-3x) \u2013 (-1) The Correct Answer and Explanation is: Let’s solve this step by step […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-33109","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33109","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=33109"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33109\/revisions"}],"predecessor-version":[{"id":33111,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33109\/revisions\/33111"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}