diff --git a/chapter05/glibc.xml b/chapter05/glibc.xml
index 34138e432..11d4cfce4 100644
--- a/chapter05/glibc.xml
+++ b/chapter05/glibc.xml
@@ -252,7 +252,7 @@ SEARCH_DIR("=/lib")
 SEARCH_DIR("=/usr/lib");</computeroutput></screen>
 
    <para>A 32-bit system may use a few other directories, but anyway
-   the important facet here is all the pathes should begin with an equal sign
+   the important facet here is all the paths should begin with an equal sign
    (<literal>=</literal>), which would be replaced with the sysroot
    directory that we've configured for the linker.</para>
 
diff --git a/part3intro/toolchaintechnotes.xml b/part3intro/toolchaintechnotes.xml
index 7afb2d9ac..a9af3c542 100644
--- a/part3intro/toolchaintechnotes.xml
+++ b/part3intro/toolchaintechnotes.xml
@@ -245,7 +245,8 @@
           example, when building an utility natively, its man page can be
           generated by running the utility with the
           <parameter>--help</parameter> switch and processing the output,
-          but generally it's not possible to do so as the utility may fail
+          but generally it's not possible to do so for a cross-compilation
+          as the utility may fail
           to run on <quote>the build</quote>: it's obviously impossible to
           run ARM64 machine code on a x86 CPU (without an emulator).
         </para>
@@ -253,7 +254,7 @@
           With an autoconf-based build system, this requirement is
           satisfied in <quote>the cross-compilation mode</quote> where
           the optional features requiring to run machine code for
-          <quote>the host</quote> are disabled.  When <quote>the
+          <quote>the host</quote> during the build time are disabled.  When <quote>the
           host</quote> triplet is explicitly specified, <quote>the
           cross-compilation mode</quote> is enabled if and only if either
           the <command>configure</command> script fails to run a dummy
@@ -302,7 +303,7 @@
     <command>libtool</command>, a <quote>compatibility</quote> wrapper of
     the compiler and the linker for autoconf-based build systems,
     can try to be too clever and mistakenly pass options allowing the linker
-    to find libraries of <quote>the host.</quote>
+    to find libraries of <quote>the build.</quote>
     To prevent this fallout, we need to delete the libtool archive
     (<filename class='extension'>.la</filename>) files and fix up an
     outdated libtool copy shipped with the Binutils code.</para>
@@ -360,8 +361,7 @@
     during stage 2.  As we've discussed, we cannot run cc-lfs on pc (the
     host distro) because it may require some library, code, or data not
     available on <quote>the build</quote> (the host distro).
-    So when we build gcc stage 2, we instruct the building system to
-    rebuild libgcc and libstdc++ with cc1, but we also override the library
+    So when we build gcc stage 2, we override the library
     search path to link libstdc++ against the newly
     rebuilt libgcc instead of the old, degraded build.  This makes the rebuilt
     libstdc++ fully functional.</para>